Management Estimates of Cost of Capital

Vincent Y.S. Chen* NUS Business School

National University of Singapore Email: bizvcys@nus.edu.sg

TEL: + (65) 6516-7815 FAX: + (65) 6773-6493

Bin Miao NUS Business School

National University of Singapore Email: miaobin@nus.edu.sg

TEL: + (65) 6516-3083 FAX: + (65) 6773-6493

Abstract: This study empirically examines the cost of capital employed by company management in their asset valuation decisions. Using a sample of cost of capital estimates manually collected from firms’ 10-K filings, we find that several firm characteristics, such as firm age, financial leverage, cash holding, and cash flow volatility, are among the important determinants of firms’ overall cost of capital. Further, management estimates of cost of equity are correlated with firm size, CAPM beta, and momentum, but not with book-to-market ratio or popular estimates derived from market data and valuation models (e.g. PE, PEG, or MPEG ratio). Finally, we find that cost of capital has a significant impact on investment, with 1% increase in cost of capital reducing the firm’s average annual capital expenditure over the next three years by $7 million.

JEL Classification: G30; G31; G32

Keywords: Cost of Capital; Capital Budgeting; Financing Policy

* Corresponding author. We thank Dan Dhaliwal, and workshop participants at the 2010 American Accounting Association Annual Meeting, and National University of Singapore for comments. All errors are our own.

Management Estimates of Cost of Capital

Abstract: This study empirically examines the cost of capital employed by company management in their asset valuation decisions. Using a sample of cost of capital estimates manually collected from firms’ 10-K filings, we find that several firm characteristics, such as firm age, financial leverage, cash holding, and cash flow volatility, are among the important determinants of firms’ overall cost of capital. Further, management estimates of cost of equity are correlated with firm size, CAPM beta, and momentum, but not with book-to-market ratio or popular estimates derived from market data and valuation models (e.g. PE, PEG, or MPEG ratio). Finally, we find that cost of capital has a significant impact on investment, with 1% increase in cost of capital reducing the firm’s average annual capital expenditure over the next three years by $7 million.

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Management Estimates of Cost of Capital

1. Introduction

Cost of capital is fundamental to a firm’s investment and financing decisions. As learned

from textbooks, cost of capital directly affects a firm’s choice of financing and capital structure,

and influences a firm’s investment decisions through the setting of hurdle rates. Cost of capital

is also essential to asset pricing as many of the valuation methodologies require it as a key input

for discounting future cash flows.

Given its importance, a large body of accounting and finance literature has been devoted

to studying cost of capital and its determinants. Several approaches have been developed to

estimate cost of equity capital, such as the Capital Asset Pricing Model (CAPM) of Lintner

(1965) and Sharpe (1964), Arbitrage Pricing Theory (APT) of Ross (1976), and methods that

back out cost of equity by inverting accounting-based valuation models (e.g. Claus and Thomas,

2001; Gebhardt et al., 2001; Easton et al., 2002; Easton, 2004). These studies mostly use price

and return data from stock market and hence the resulting cost of capital estimates reflect the

view of investors.

In this paper, we take a different approach to study cost of capital by empirically

examining the cost of capital estimates that reflect company management’s view. Specifically,

we collect from companies’ financial reports the cost of capital estimates used by managers in

asset valuation decisions, and examine their characteristics and how they are related to cost of

capital estimated from market data. Studying the management’s estimates of cost of capital is

important for several reasons. First, cost of capital is a critical input to many corporate decisions

that jointly determine the fundamental value and growth prospect of a firm (Copeland et al.,

2005; Penman, 2007; and Brealey et al., 2008). As such, examining the cost of capital directly

used by the decision makers provides a new perspective that will help us better understand the

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role of this information in those decisions. Second, the inherent asymmetry of information

between managers and investors suggests that the two parties’ estimates of cost of capital are

likely to diverge, as they are conditional on different information sets. Hence, it is inappropriate

to use estimates implied solely by market price as proxy for managers’ belief. Finally, limitations

on data and methodology cause empirical estimates of cost of capital from market data to be

contaminated by measurement errors, which under certain circumstances may lead to spurious

conclusions (Easton and Sommers, 2007). In contrast, the cost of capital used by management

examined in this study is largely free of such problems, as the data are directly collected from

companies’ published reports.

We obtain management estimates of cost of capital from 10-K reports. Under some

accounting standards, a firm is required to conduct discounted cash flow analysis and thus it is

necessary for the firm to estimate a discount rate, which in most cases is the firm’s cost of capital.

For example, Statement of Financial Accounting Standard 142 (SFAS 142) requires a firm that

carries goodwill balance to conduct goodwill impairment tests periodically, in which the firm has

to determine whether an impairment loss is incurred by comparing fair value with book value of

goodwill. To estimate the fair value of goodwill, the firm is recommended to use a discounted

cash flow model when the market value of goodwill is not available.1 While SFAS 142 does not

mandate the disclosure of the discount rates used in such analysis, some companies choose to do

so voluntarily in their annual reports, thus making our empirical analyses of this information

possible.2

1 Other standards that require a firm to conduct a discounted cash flow analysis include tests of impairments and recoveries of intangible assets (SFAS 121, 142 and 144). 2 Auditors are held responsible for footnote disclosures and assumptions reported in firms’ 10-K reports. For example, Statement on Auditing Standards (SAS) No. 101, which provides auditors guidance for auditing fair value measurements and disclosures, requires auditors to evaluate whether the assumptions (such as discount rate) used in the valuation model are reasonable.

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Our sample consists of 307 firm-year observations from 2001 to 2008. The mean (median)

overall cost of capital of our sample firms is 13.3% (12.3%).3 We then investigate the cross-

sectional variation of the sample firms’ cost of capital and find that certain firm characteristics,

such as firm age, financial leverage, cash holdings, and cash flow volatility, are among the

important factors that influence managers’ cost of capital estimates. In particular, the overall cost

of capital is higher for firms with shorter history of operation, lower financial leverage, higher

cash holding, and more volatile cash flows, all of which are consistent with economic intuition

and supported by finance theories (e.g., Fama and French, 1992; Minton and Schrand, 1999; and

Opler et al., 1999; Modigliani and Miller, 1963; and Myers and Majluf, 1984).

In contrast to cost of debt, studies of cost of equity have taken the central stage of much

of the finance and accounting literature, probably due to the inherent difficulty of obtaining

accurate estimates.4 The influential CAPM introduces systematic risk (beta) as the only firm-

specific factor that determines a firm’s cost of equity. In addition to CAPM beta, prior research

has also identified firm size, book-to-market ratio, and momentum as empirical “risk factors”

that drive variation in cost of equity.5 On the other hand, CAPM beta as an empirical determinant

of cost of equity has found little support from historical data, while the debate has never abated

over whether the other “risk factors” are really firm characteristics that happen to be correlated

with co-movements in stock return (e.g., Daniel and Titman, 1997). Our dataset provides a 3 We note this figure is significantly higher than the overall cost of capital estimated by Fama and French (1999). It is also higher than the cost of equity estimates provided by prior studies that use the discounted cash flow valuation approach or asset-pricing model approach. For example, both Claus and Thomas (2001) and Gebhardt et al. (2001) document that risk premiums over their sample periods are about 3 percent, while Easton et al. (2002) report risk premium over their sample period is about 5.3 percent, which is close to the estimate of 4.5 percent in Fama and French (2002). The risk free rates (10-year treasury bond) for our sample period range from 2.42% to 6.66%, averaging at 4.59%. To the extent that a firm’s overall cost of capital is lower than cost of equity capital because of the tax advantage of interest expenses, our findings suggest the cost of equity capital used by managers may be much higher than researchers’ estimates. 4Broader data availability could be another reason for the disproportionally large number of studies of equity markets. 5 Strictly speaking, these factors have been shown to be correlated with future realized return. Elton (1999) points out that realized return is a poor proxy for expected return or cost of equity.

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unique opportunity to re-examine this longstanding issue from a new perspective. By directly

examining the cost of equity estimates used by managers, we are able to evaluate the importance

of these factors in affecting cost of equity, at least from company management’s point of view,

and hence the related financing and investment decisions. We find that management’s estimates

of cost of equity is negatively associated with firm size and positively associated with CAPM

beta. Moreover, managers tend to lower their estimates of cost of equity when their companies’

stock experience recent run-up, suggesting that they do not view short-term momentum as risk

factor. Finally, we find no evidence that book-to-market ratio affects cost of equity estimated by

management.

Another method commonly used in prior studies to estimate cost of equity is to “invert”

a particular discounted cash flow (DCF) valuation model to find out the “implied” cost of equity

(Claus and Thomas, 2001; Gebhardt et al., 2001, Easton et al., 2002, Easton, 2004). 6 We

calculate cost of equity for our sample firms using this method and compare them with those

used by management. Because the firms in our sample rarely disclose their cost of equity

estimates, we assume a simple capital structure and a constant tax rate to filter out the impact of

after-tax cost of debt from our weighted average cost of capital data. We examine three

variations of DCF valuation model, PE, PEG, and MPEG, and find that management’s estimates

of cost of equity are significantly higher than the estimates from all three methods. Further, and

somewhat to our surprise, none of the DCF estimates is reliably correlated with managers’

estimates. While it is always a possibility that the power of our test is restricted by the relatively

small sample size, our results suggest there may be fundamental differences between “implied”

cost of capital and the cost of capital used by managers in their actual decision-making process.

6 This method does not rely on a specific risk-factor pricing model, but requires estimation of the market’s expectation for future pay-offs over an infinite period, which in many cases involves significant measurement errors that result in systematically biased cost of equity estimates (Easton and Sommers, 2007).

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Taken together, our analyses suggest that managers are more in favor of factor asset pricing

model approach in estimating cost of equity, though their choice of the specific set of risk factors

is likely to differ from those found in academic literature.

The final part of the paper examines the impact of a firm’s cost of capital on its

investment level. We find that firms with more expensive source of capital invest significantly

less on long-term physical assets, with 1% increase in cost of capital reducing the firm’s average

capital expenditure over next three years by 0.09% of total assets, which amounts to about 7

million dollars per year for our sample firms. Further, this relation remains largely unaffected by

the inclusion of other factors that influence investments, such as growth opportunities (measured

by Tobin’s Q) and the availability of internally generated cash flows.

Our paper contributes to the cost of capital literature on two fronts. First, to the best of

our knowledge, we are the first study that empirically examines the cost of capital used by

company managements of firms from a wide cross-section of industries. This fills a void in

existing literature, which has mainly focused on estimating the return on investments required by

equity investors. Second, our paper adds to survey studies of managers’ choice of cost of capital,

such as Graham and Harvey (2001) and Poterba and Summers (1995). While both of the studies

reveal numerous interesting findings on firms’ capital budgeting practices, our study, by

examining cost of capital estimates that are part of the actual managerial decision-making

process, complements these studies and extends them by providing evidence on issues that are

difficult to address through questionnaires.

The rest of the paper is organized as follows. In section two we review the institutional

background. Section three describes the data collection process, and section four discusses the

results of our empirical tests. Section five concludes.

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2. Institutional Background

Some accounting standards require firms to estimate fair value of asset or liability (e.g.,

SFAS 141, SFAS 142, etc.). When market price is not available for a particular asset or similar

assets, firms would usually have to carry out discounted cash flow analysis to estimate fair

value.7 To conduct the valuation analysis, various inputs are required and discount rate is one of

them. While it is not mandatory for firms to disclose those input information for the valuation

analysis, some firms do so voluntarily in their annual reports. Below we briefly review some of

the accounting standards that require firms to estimate fair value.

Goodwill and Non-amortizable Intangible Assets

The issuance of SFAS 142 fundamentally changed the way of accounting for goodwill.

Before SFAS 142, goodwill and intangible assets with indefinite useful-lives was systematically

amortized. After SFAS 142, those assets are no longer amortized but reviewed for impairment at

least annually. SFAS 142 also provides guidance for testing impairments of goodwill and

intangible assets with indefinite useful-lives.

Under SFAS 142, firms perform goodwill impairment tests at segment level using a two-

step process: Step 1: Compare the fair value and the book value (including goodwill) of a

reporting unit. If the fair value is less than the book value, managers perform step 2 to see if

goodwill is impaired. If the fair value exceeds the book value, step 2 is unnecessary. Step 2:

Compare the implied fair value and the book value of goodwill in the reporting unit. If the

implied fair value is less than the book value, the difference is recognized as goodwill

impairment loss. For intangible assets with indefinite useful-life, SFAS 142 states that

impairment loss is determined by comparing the book value of the asset with its fair value, where

7 Under most circumstances, it is recommended but not required for the firm to use the discounted cash flow valuation technique to estimate fair value.

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the amount of the impairment loss is equal to the excess amount of the fair value over the book

value.

To estimate fair value, SFAS 142 indicates that the best measure of fair value is market

prices from active markets, if available. The standard also states that the market price, however,

may not be representative of fair value in some circumstances.8 In a situation where market price

is not representative or not available, the estimation of fair value is needed. The statement

recommends the use of discounted cash flows to derive fair value, although it also allows other

valuation techniques, such as market multiple approach or appraisal approach. In applying the

discounted cash flow approach to estimate fair value, the management has to estimate the

discount rate reflecting the firm’s cost of capital commensurate with risk (FASB Concepts

Statement 7).

For intangible assets with definite useful-life, impairment losses are recognized and

measured in the same manner as long-lived assets, which are supervised by SFAS 144.

Therefore, we discuss the accounting treatments of impairment losses for those assets together

with long-lived assets in the next section.

Long-lived Assets

SFAS 144 directs how a firm accounts for the impairment or disposal of long-lived assets

except goodwill and intangible assets with indefinite useful-lives.9 According to the statement, a

firm is required to record an impairment loss if the firm finds that the book value of the asset is

not recoverable and exceeds its fair value. The book value is deemed as unrecoverable if the

book value of the asset is greater than the sum of the undiscounted cash flows associated with the 8 For example, some assets have to be priced in a bundle with other assets and liabilities. That is, those assets cannot be valued separately from other assets and liabilities and thus the prices for those assets are not objective and representative for fair values. 9 SFAS 144 also does not apply to long-term customer relationships of a financial institution, financial instruments, deferred policy acquisition costs, deferred tax assets, unproved oil and gas properties and to long-lived assets which are prescribed by SFAS 44, 50, 63, 86 and 90.

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asset. An impairment loss should be recorded when the book value of the asset is greater than its

fair value with an amount equal to the excess amount of the book value to the fair value.

To obtain fair value, the statement indicates that market prices from active markets are

the best measure of fair value if available. The statement also mentions that prices from similar

assets or estimated values from other valuation techniques would be measures of fair value if

market prices of assets are not available or applicable. To estimate fair value, the SFAS Concept

7 provides two approaches to estimate fair value – expected present value and traditional present

value. Under both approaches, cash flows should be discounted to the present value to obtain fair

value and thus discount rate is required and must be estimated by the management.

3. Sample Selection

We search the keywords “discount/discounted/discounting” and “cost of capital/cost of

funds” in all 10-K reports filed to SEC between 2001 and 2008 through Lexis-Nexis Academic

database.10 An initial search result of 2,950 reports is returned.11 We then carefully read each

returned 10-K reports to collect usable cost of capital data. In order to be included in our sample,

the firm must unambiguously indicate the discount rate used in valuing its goodwill or intangible

assets in compliance with SFAS 142 or 144.12 Since SFAS 142 requires the impairment test to be

performed at a segment level, we assume the discount rate reflects the project-specific cost of

capital that applies to one particular segment within the firm, unless it is explicitly indicated that

the discount rate is the firm-wide cost of capital (Sample reports are provided in Appendix A). If

a firm reports cost of capital estimates from multiple segments, we calculate a single cost of

capital estimate for each firm-year by averaging all project-specific cost of capital estimates

10 We start our sample in 2001 because SFAS 142 and 144 were both issued in 2001. 11 The text of keyword search is (((discount! w/p (cost of capital or cost of fund)) AND EXCHANGE(NYSE or NASDAQ or AMEX) and DOCUMENT-DATE AFT(January 1, 2001) and DOCUMENT-DATE BEF(May 31, 2009))). 12 If the firm discloses a range of discount rates we use the mid-point of the range as the discount rate.

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disclosed by a firm during the same year. We then merge these firms with CRSP and

COMPUSTAT databases to get required accounting and market data. Our final sample consists

of 307 firm-year cost of capital estimates from 205 unique firms, of which 77 are firm-wide cost

of capital and 230 are project-specific cost of capital.13

4. Empirical Results

4.1 An overview of sample firms’ cost of capital

Panel A of Table 1 presents descriptive statistics of the sample. Compared with the

COMPUSTAT database, our sample tends to include larger firms, as consistently indicated by

various measures such as book value of total assets, sales, and market capitalization. Our sample

firms also hold higher levels of intangible assets. The median values of intangible assets and

goodwill as a percentage of total assets for our sample firms are 0.29 and 0.19, respectively,

compared with those of 0.04 and 0.02 for the median COMPUSTAT firm. These differences,

however, is not unexpected because the cost of capital estimates were collected from the firms

that conduct impairment tests for their existing intangible assets and goodwill. Finally, the firms

in our sample are more highly levered with median market leverage ratio of 0.30, compared to

that of 0.13 for all COMPUSTAT firms.

Panel B shows that the mean (median) cost of capital of the sample firms is 13.3 percent

(12.3 percent), ranging from as low as 6.7 percent to as high as 45 percent. When we further

break down the full sample into project-specific and firm-wide cost of capital, we find that

managers’ estimates of project-specific cost of capital are on average higher than their estimates

of firm-wide cost of capital (13.9% v.s. 11.6%). This difference is consistent with the

coinsurance effect among a diversified firm’s different segments reducing the firm’s overall

systematic risk, as argued in Hann et al. (2010).

13 Sample size may vary in subsequent analyses due to different data requirements.

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Table 2 reports the industry distribution of our sample. 14 Using COMPUSTAT as

benchmark, our sample has a higher concentration in Business Equipment and Manufacturing

industries, and a significant under-representation of Finance industry, which accounts for only

5.9% (v.s. 32.2% in COMPUSTAT) of all sample firms. This is because many firms in the

Finance industry have special sources of funds (e.g., banks and insurance companies), and as a

result we exclude a significant portion of those firms during the data collection process.

Consistent with prior studies of industry cost of equity using market data (Fama and

French 1997, Gebhardt et al. 2001), we find a significant variation in management estimates of

cost of capital across industries. In particular, firms in the Business Equipment industry report

the highest average cost of capital (16.6%), while Utility companies enjoy the lowest financing

cost (10%). This may reflect the difference in industry-wide risk profile, but could also be driven

by other firm-specific factors that vary systematically across industries.15 Overall, as reported in

Panel B, industry affiliation explains 18.3% of variations in our sample firms’ cost of capital.

Table 3 reports the temporal variation of cost of capital, and its correlation with measures

of market-wide cost of debt and equity. We use 10-year moving average of return on the S&P

500 index as measure for “realized” historical cost of equity and calculate an “implied” cost of

equity for the market by averaging the implied cost of equity16 for all firms estimated at the

beginning of each calendar year. For measures of market-wide cost of debt we use the average

yields on all S&P rated investment grade bond and speculative grade bonds. These data were

obtained from the RatingsDirect® database maintained by S&P and were only available since

14 We use Fama-French 12 industry classification. http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html . 15 We explore this possibility in further detail in section 4.2. 16 We use the PEG approach to estimate the implied cost of equity where epst is the earnings

forecast for year t and Pt is the price at the end of year t. Botosan and Plumlee (2005) evaluate several alternative methods of estimating cost of equity capital and conclude that the performance of PEG is better than others.

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2003. While our sample spans a relatively short period of 8 years, which unavoidably limited the

scope of our time-series analysis, we note that several interesting patterns are apparent from the

data. First, our sample period covers two recessions in 2001 and 200817, and in both years we see

a clear spike in firms’ overall cost of capital. In particular, during the recent financial crisis the

average funding cost of our sample firms increased by 2.6%, from 11.6% in 2007 to 14.2% in

2008. Second, the temporal changes in cost of capital exhibit virtually no correlation with recent

stock market performance or the expected return implied by current stock market valuation,

suggesting that managers’ assessment of cost of equity are likely to differ from the view

expressed by investors. In contrast, managers’ estimates of cost of capital closely follow

developments in bond yield, exhibiting a correlation of 0.84 (0.92) with S&P investment

(speculative) grade bond yield. This simple comparison suggests that when estimating their firms’

cost of capital, managers tend to place more weight on market signal of cost of debt than cost of

equity.

4.2 Cross-sectional determinants of overall cost of capital

In this section, we examine the cross-section of management estimates of overall cost of

capital and its determinants. Drawing on prior research, we include the following candidate

variables in our test: firm size (SIZE), firm age (AGE), Tobin’s Q (Q), cash holdings (CASH),

cash flow volatility (σ(CFO)), effective tax rates (TAX), financial leverage (LEV), cash flows

from operations (CFO5), and earnings before interest and tax expenses (EBIT).18 SIZE and AGE

capture a firm’s stage in lifecycle and hence its business risk (e.g., Fama and French, 1992). Q,

CASH, and σ(CFO) are associated with a firm’s ex ante demand for external financing (e.g.,

Minton and Schrand, 1999; and Opler et al., 1999). TAX and LEV are related to a firm’s capital

17 NBER identifies the two recessions as March 2001 – November 2001 and December 2007 – June 2009. 18 All variables are measured to lead cost of capital estimates by one year.

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structure, and CFO5 and EBIT measure a firm’s financial performance. To mitigate the impact of

outliers and nonlinearity of the co-variation among variables, we replace the variables with their

respective decile rankings within the CRSP universe in our correlation and multivariate

regression analysis.

As shown in the correlation matrix in Panel A of Table 4, a firm’s overall cost of capital

is significantly correlated with the characteristics identified above, and with predicted signs. For

example, cost of capital is negatively associated with firm SIZE and AGE, consistent with the

intuition that firms with higher business risk tend to have higher cost of equity capital (e.g.,

Fama and French, 1992). We find a positive correlation between cost of capital and Q, σ(CFO),

and CASH, consistent with the prior literature that firms with more investment opportunities,

higher information asymmetry, and more frequent access to external capital market will have

higher cost of capital (e.g., Calomiris et al., 1995; Minton and Schrand, 1999; Opler et al.,

1999).19 Further, cost of capital is lower for firms with higher effective tax rate and leverage due

to the tax benefits of interest expense and lower cost of debt financing (e.g., Modigliani and

Miller, 1963; Myers and Majluf, 1984). Finally, we find firms with better financial performance

(as measured by CFO5 and EBIT) enjoy lower cost of capital.

Panel B of Table 4 reports the multivariate regression results. In addition to the firm

characteristic variables we also include a binary variable indicating whether the cost of capital is

firm-wide or project-specific, as we found in earlier analysis that managers’ estimates of project-

specific cost of capital are generally higher. The regression coefficients on the explanatory

variables all exhibit consistent signs with those in bi-variate correlations, but only firm age, cash

19 Minton and Schrand (1999) argue that firms with higher cash flow volatility are more likely to face cash flow shortfalls and thus have to use external capital to fund their investments, which drives up cost of capital. Calomiris et al. (1995) and Opler et al. (1999) argue that firms with poor access to capital markets tend to hold more cash as a self-insurance device. Note that by their argument, the causal relationship between cash holding and cost of capital should be anticipation of high cost of capital driving managers to hold more cash, instead of the other way round.

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holding, leverage, and cash flow volatility show statistically significant impact on cost of capital.

These four variables, together with the firm-wide dummy, explains 38% of total variation in the

dependent variable, suggesting managers consider them as important factors that affect firms’

overall cost of capital.

4.3 Determinants of cost of equity capital

In contrast to cost of debt, existing studies of cost of capital have mostly centered on the

measurement of cost of equity, probably due to the inherent difficulty of obtaining accurate

estimates. Prior literature has suggested that cost of equity is associated with several risk factors,

such as firm size, book-to-market ratio, CAPM beta, and past returns (Fama and French, 1993;

Carhart, 1997). In this section, we examine the role of these factors in management’s estimates

of cost of equity capital. Insights from such analyses would be interesting for two reasons. First,

to the extent that the information sets of external investors and corporate insiders do not fully

converge, cost of equity estimated using market price data, which reflect the view of external

investors, is unlikely to be a perfect proxy for managers’ own assessment of cost of equity. By

directly examining the cost of equity estimates used by managers, we will be able to better

understand how these risk factors influence corporate financing and investment decisions.

Second, it remains an unsettled issue in finance literature whether variables such as book-to-

market ratio and momentum are indeed risk factors or just firm characteristics that happen to be

correlated with stock returns (Daniel and Titman, 1997). If managers are on average better

informed than external investors about the risk profile of their company, our analyses of

management estimates of cost of equity may contribute to solving this longstanding puzzle.

The basic construct of our analyses is a multivariate regression model. Since our sample

data are mostly overall cost of capital, we must control for effects of leverage and cost of debt to

isolate the cost of equity capital. We develop the empirical approach as follows. We start with

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the weighted-average cost of capital (WACC) equation and express WACC as a function of

assets, debt, equity, tax rate, cost of debt and cost of equity: 20

1 (1)

We assume that cost of debt (KD) and cost of equity (KE) can each be expressed by a linear factor model, respectively:

∑ (2)

∑ (3)

For simplicity, we define 1 and 1 . We plug (2) and (3) into (1)

and get (5):

∑ 1 ∑ (4)

After rearranging the equation and assuming a constant tax rate across firms, we get the following model for regression analyses:

∑ ∑ 1 (5)

where

WACC = Weighted-average cost of capital;

Di = Factors that determine cost of debt;

Ei = Factors that determine cost of equity;

L = Leverage ratio.

20 We make a simplifying assumption that all firms have only debt and common equity components in the capital structure.

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We use S&P long-term credit rating as our proxy for cost of debt21. For cost of equity

determinants, we include CAPM beta, firm size, book-to-market ratio, and momentum as risk

factors (Fama and French, 1993; Carhart, 1997). The results are reported in Table 5. Our sample

size is reduced to 91 due to the additional data requirement, mainly the use of S&P credit rating

as the proxy for cost of debt. In the regression analysis, we translate the letter grade credit rating

into numerical scores, with 1 representing AAA and 10 representing D.22 We also replace the

cost of equity risk factors (size, beta, the book-to-market ratio, and momentum) with their

respective decile rankings within the CRSP universe.

We find that the coefficient on leverage is negative and highly significant across all

model specifications, consistent with the intuition that weighted-average cost of capital decreases

in the degree of leverage because after-tax cost of debt is lower than cost of equity.23 We also

find the coefficients on credit rating (interacted with leverage ratio) are consistently positive with

high statistical significance, suggesting that it is an effective control for cost of debt. For our

main variables of interest, the results show that firm size, CAPM beta, and short-term stock price

momentum (all interacted with one minus leverage ratio) are significantly correlated with cost of

equity capital, while the book-to-market ratio is not. The result on CAPM beta is particularly

interesting. Consistent with the survey evidence of Graham and Harvey (2001), our analyses

suggest that, despite the many criticisms, CAPM is still an important method that managers rely

on to gauge their cost of equity capital. However, the results also suggest managers do not apply

CAPM in a manner that is strictly consistent with its theoretical development, which allows

systematic risk (beta) as the only firm-specific determinant of cost of equity. In particular, the

21 Hand et al. (1992) find that S&P’s credit rating changes are associated with changes in bond prices, and Calomiris et al. (1995) find that firms with more favorable S&P rating have better access to commercial paper markets. 22 The remaining rating-score translations are: AA~2, A~3, BBB~4, BB~5, B~6, CCC~7, CC~8, C~9 23 The pecking order theory (Myers and Majluf, 1984) argues that debt financing tends to be less expensive than equity.

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finding that firms with larger market capitalization have lower cost of equity is inconsistent with

CAPM, but is in line with the conventional argument that size is related to a firm’s underlying

risk and accessibility to external financing. In addition, the result that recent stock price

performance has a contrarian effect on managers’ estimate of cost of equity may seem surprising,

especially given the well-known phenomenon that share price tends to continue its recent

momentum into the near future, but on the other hand is consistent with the strategic market

timing hypothesis for equity issuance. (Marsh 1982, Jung et al. 1996)

Taken together, our analyses in this section suggest managers’ approach to estimating

cost of equity is more consistent with a multi-factor asset pricing model, but their choice of

specific risk factors are likely to be different from those found in the academic literature.

4.4 Alternative estimates of cost of equity capital

As an alternative to the factor asset pricing model approach, prior studies of cost of

equity have also developed empirical measures of “implied” cost of capital by using various

accounting-based valuation models (e.g. Claus and Thomas, 2001; Gebhardt et al., 2001; Easton

et al., 2002; Easton, 2004; Ohlson and Juettner-Nauroth, 2005). In this section we compare these

model-implied measures of cost of equity with company management’s estimates. In particular,

we examine three alternative estimates using the PE, PEG, and MPEG approach.24 We assume a

constant tax rate of 40% and a simple capital structure consisting of only debt and equity, and

calculate the firm’s weighted average cost of capital using the following equation:

24 Under the PE approach, cost of equity (rPE) is implied by . Under the PEG method, cost

of equity (rPEG) is calculated as . Under the MPEG approach, cost of equity (rMPEG) is implied by

, where epst+1 and epst+2 are the earnings forecast for year t+1 and t+2, respectively, both

measured in December of year t. Pt is the price at the end of year t, and dpst is dividend per share paid in year t.

17

0.6 1

(6)

where KD is cost of debt, estimated using the average bond yield of all firms within the

same S&P rating category as the current firm. 25 D is book value of long-term debt, A is the

sum of book value of long-term debt and market value of common equity, KE is cost of equity

capital estimated using the PE, PEG, or MPEG approach.

Due to the additional requirement of analyst forecasts and bond yield data, our sample

size is reduced to 46. As reported in Panel A of Table 6, the weighted-average cost of capital

estimates derived from the valuation model approach range from 5.3% to 8.7%, which are

consistently lower than those estimated by company management (10.4%). In addition, both

PEG and MPEG estimates of overall cost of capital exhibit positive, albeit weak, correlations

with managers’ estimates. However, since these figures combine both the effects of cost of debt

and equity, it is too early to conclude that PEG and MPEG estimates of cost of equity are more

closely related to managers’ estimates. To purge the debt component from overall cost of

capital, we adopt a similar approach as in section 4.3, and replace the equity risk factors in

equation (5) with one of the estimates from the PE, PEG, or MPEG method. The multivariate

regression results in Panel B of Table 6 show that, after controlling for the impact of leverage

and S&P credit rating, none of valuation-model-implied estimates of cost of equity is reliably

related to management’s estimates of cost of capital. Aside from the possibility that the power

of our test is restricted by the relatively small sample size, these results suggest there may be

fundamental differences between “implied” cost of capital and the cost of capital used by

25 The analyst forecast and bond yield data were collected from the I/B/E/S and S&P RatingsDirect® databases, respectively.

18

managers in their actual decision making process. Instead, our analyses suggest managers are

more in favor of using the multi-factor asset pricing model approach to estimate cost of equity.

4.5 Investment and cost of capital

Standard finance textbooks have established that cost of capital is a fundamental piece of

capital budgeting decision and thus affects the firm’s investment (e.g., Copeland et al., 2005).

Loosely speaking, for a firm whose available investment opportunities are not mutually

exclusive, its investment level should be an inverse function of its cost of capital, other things

being equal. Compared with cost of capital estimated by market data, our sample of cost of

capital that reflect company management’s estimates provides an ideal opportunity to

empirically examine this prediction, because arguably the cost of capital estimates and

investment decisions are both made by the same party.

The results in Panel B of Table 7 show that a firm’ cost of capital has a major impact on

its investment level. In particular, firms with more expensive source of capital invest

significantly less on long-term physical assets. By our estimate, 1% increase in cost of capital

reduces the firm’s average capital expenditure over next three years by 0.09% of total assets,

which for our sample firms amounts to about 7 million dollars per year.26 In additional analyses,

we control for firms’ investment opportunity sets (measured by Tobin’s Q) and internal

financing capability (measured by average operating cash flows over the past five years), both of

which have been suggested by prior research as important determinants of corporate investment

(e.g. Fazzari et al., 1988). Our results are robust to these alternative model specifications.

5. Conclusion and discussion

We add to the cost of capital literature by studying management estimates of cost of

capital. Using a sample of cost of capital estimates manually collected from firms’ 10-K filings,

26 The average total assets for our sample firms for this test is 7.64 billion (untabulated).

19

we find that several firm characteristics, such as firm age, financial leverage, cash holding, and

cash flow volatility, are among the important determinants of firms’ overall cost of capital.

Further, management’s estimates of cost of equity are correlated with firm size, CAPM beta, and

momentum, but not with book-to-market ratio or cost of equity “implied” by various accounting-

based valuation models (e.g. PE, PEG, or MPEG ratio). Finally, we find that cost of capital has a

significant impact on corporate investment.

The findings of our study suggest that there may be fundamental differences between

managers’ choice of cost of capital and estimates derived from market data and popular valuation

models, which have important implications for understanding manager’s investment and

financing decisions. It is our maintained assumption that the difference arise from investors’ and

managers’ divergent views on cost of equity, because it is generally easier to obtain accurate

estimates of, and hence to agree on the cost of debt. In theory, cost of equity should reflect the

return demanded by equity investors on their investment in the firm, and therefore the cost of

equity used by managers should be their best estimates of investors’ demand. By such reasoning,

any deviation from the market’s expected return will lead managers to make suboptimal

decisions and hence should be avoided. On the other hand, it is usually extremely difficult, if not

impossible at all, to develop a perfect estimate of expected return. So the difference may as well

be the joint result of multiple forces, such as the information asymmetry between management

and investors, or the inadequacy of current estimation methodology of cost of equity. Regardless

of its cause, the difference itself suggests that the study of management’s estimate of cost of

capital offers promising opportunities for future research that seek to understand managerial

behavior and corporate finance decisions.

20

Like most of the studies that employ hand-collected data, our study has a modest sample

size and hence is subject to potential limitations on the generalizability of our findings. However,

as discussed in section 4.1, while our sample covers a relatively short time period, it spans a wide

cross-section of industries and does not exhibit significant idiosyncracy in most of the major firm

characteristics. Therefore, while unable to verify that the firms examined in our study are drawn

through a random process, we are also unaware of any peculiarity of the sample that would bias

our results in a systematic way. Another concern is that the discount rates we collected may

actually reflect the hurdle rates that were set by managers with discretion, and hence may not

track the firms’ cost of capital perfectly. While it is certainly a possibility that a manager’s

choice of discount rates could deviate from her estimates of cost of capital due to certain

strategic considerations or agency problem, it needs not to have any material impact on our

results because the focus of our study is on the determinants of cross-sectional variation in cost

of capital, rather than the magnitude of cost of capital per se. For this reason, we allow the

discount rates to track cost of capital with error, as long as the errors are random and do not

consistently co-vary with the firm characteristic variables that were examined in our tests.

Finally, in this study we examine only factors that are grounded in economic theory, while

leaving out the role of any personal attributes or human heuristics in affecting the manager’s

estimate of cost of capital.27 We believe it is an interesting question, and leave it for future

research to answer.

27 Prior studies have documented that managers differ in skills, preferences, risk aversion, and reputation, and that these characteristics affect corporate accounting, financing and investing decisions (e.g., Graham and Harvey, 2001; Bertrand and Schoar, 2003; Aier et al., 2005).

21

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24

Appendix A Sample disclosures of firms’ cost of capital

1. Firm-wide cost of capital

Eddie Bauer Holdings (2008, 10-K, emphasis added)

Our goodwill impairment test was completed using the two-step approach prescribed in SFAS 142. The first step included a determination of the enterprise value of the Company using a discounted cash flow model which included our five-year long-range plan related to the future cash flows of our primary assets; a discount rate of 17.0%, which represented our weighted average cost of capital; and a terminal value growth rate of 3.0%. In order to assess the fair value of the Company in its entirety, following the calculation of the discounted cash flows of our primary assets, the book value of our interest-bearing debt was deducted and the fair values of the assets not contributing to the discounted cash flows of our primary assets, including our net operating loss carryforwards, were added to derive the fair value of our total net assets. Upon completion of step one of the goodwill impairment test, the estimated fair value of the Company was less than the carrying value of our net book value and long-term debt. Accordingly, we completed step two of the goodwill impairment test, which included comparing the implied fair value of the Company with the carrying amount of goodwill. Upon completion of step two of the goodwill impairment test, we recorded an impairment charge of $64.6 million related to our goodwill. Consistent with the decline in the fair value of our trademarks, the decline in our enterprise value since the prior year-end was driven by the overall downturn in the economy and projected continued declines in consumer retail spending. 2. Project-specific cost of capital

FEDEX CORP (2008 10-K, emphasis added)

We performed our annual impairment testing in the fourth quarter for the Kinko’s trade name and the recorded goodwill for the FedEx Office reporting unit. In accordance with the accounting rules, the trade name impairment test was performed before the goodwill impairment test.

In accordance with SFAS 142, “Goodwill and Other Intangible Assets,” a two-step impairment test is performed on goodwill. In the first step, we compared the estimated fair value of the reporting unit to its carrying value. The valuation methodology to estimate the fair value of the FedEx Office reporting unit was based primarily on an income approach that considered market participant assumptions to estimate fair value. Key assumptions considered were the revenue and operating income forecast, the assessed growth rate in the periods beyond the detailed forecast period, and the discount rate.

In performing our impairment test, the most significant assumption used to estimate the fair value of the FedEx Office reporting unit was the discount rate. We used a discount rate of 12.5%, representing the estimated weighted-average cost of capital (“WACC”) of the FedEx

25

Office reporting unit. The development of the WACC used in our estimate of fair value considered the following key factors:

• benchmark capital structures for guideline companies with characteristics similar to the FedEx Office reporting unit;

• current market conditions for the risk free interest rate;

• the size and industry of the FedEx Office reporting unit; and

• risks related to the forecast of future revenues and profitability of the FedEx Office reporting unit.

The WACC used in the estimate of fair value in future periods may be impacted by changes in market conditions (including those of market participants), as well as the specific future performance of the FedEx Office reporting unit and are subject to change, based on changes in specific facts and circumstances.

26

Appendix B Definition of Variables

AT Total assets (AT#)

SALE Sale (SALE#)

DTL Total long-term debt (DLTT#+DD1#)

MV_EQ Market value of common equity (PRCC_F#*CSHO#)

SIZE Firm size (DTL+MV_EQ)

LEV Leverage (DTL/MV)

Q Tobin’s Q (SIZE/(DTL+CEQ#))

BTM Book-to-market ratio of common equity (CEQ#/MV_EQ)

CASH Cash balance divided by total assets (CHE#/AT)

ROA Income before extraordinary items divided by total assets (IB#/AT)

CFO Cash flow from operations divided by total assets (OANCF#/AT)

CFO5 Average operating cash flow (CFO) over the most recent 5 years before current fiscal year

IA Intangible assets divided by total assets (INTAN#/AT)

GW Goodwill divided by total assets (GDWL#/AT)

EBIT Earnings before interest and tax, divided by total assets (OIADP#/AT)

TAX Effective tax rate, measured by income tax divided by pretax income (TXT#/PI#)

FIRM_AGE Firm age, measured by the number of years since the firm first appears in CRSP

σ(CFO) Cash flow volatility, measured by standard deviation of CFO over most recent 5 years.

BETA CAPM Beta measured over the most recent calendar year before current fiscal year end.

RET Average annual return over the most 3 calendar years before current fiscal year end.

RATING S&P long-term credit rating converted into scale of 1-10, with 1=AAA and 10=D

PE Cost of equity estimated using PE approach

PEG Cost of equity estimated using PEG approach

MPEG Cost of equity estimated using Modified PEG approach

CAPX Average capital expenditure divided by total assets (CAPX#/AT) over the 3 years immediately after current fiscal year

# COMPUSTAT mnemonics

27

Table 1 Summary Statistics

Panel A Descriptive Statistics of Sample Firms

Variable N Mean Median Std Dev Q1 Q3 COMPUSTAT

Median

AT 307 7165.80 1241.63 30319.57 399.05 4983.10 421.04

SALE 307 3372.92 938.45 6380.34 314.80 3443.00 231.64

DTL 307 1483.58 378.34 3061.50 42.11 1306.36 41.11

MV_EQ 307 3498.80 723.19 7083.49 231.73 3068.26 334.63

SIZE 307 4982.39 1199.23 9351.66 390.36 4957.05 451.10

LEV 307 0.32 0.30 0.25 0.10 0.50 0.13

Q 307 1.68 1.27 2.33 1.00 1.79 1.59

BTM 307 0.81 0.65 1.11 0.39 1.00 0.50

CASH 307 0.13 0.08 0.16 0.02 0.18 0.10

ROA 307 -0.12 0.01 0.44 -0.12 0.04 0.02

CFO 307 0.06 0.07 0.11 0.03 0.11 0.06

IA 305 0.31 0.29 0.23 0.12 0.46 0.04

GW 291 0.23 0.19 0.18 0.09 0.35 0.02

EBIT 306 0.00 0.07 0.41 0.02 0.13 0.07

TAX 307 0.09 0.24 1.68 0.00 0.36 0.26

AGE 307 18.21 13.00 16.50 6.00 26.00 10.00

σ(CFO) 307 0.06 0.04 0.06 0.02 0.07 0.05

Panel B Cost of Capital

N Mean Median Std Dev Q1 Q3 Max Min

ALL 307 0.133 0.123 0.046 0.100 0.150 0.450 0.067

Project-specific

230 0.139 0.130 0.046 0.110 0.155 0.450 0.068

Firm-wide

77 0.116 0.103 0.043 0.085 0.130 0.300 0.067

Notes to Table 1: the sample spans from 2001 to 2008. See Appendix B for variable definitions.

28

Table 2 Industry Cost of Capital

Panel A Cost of Capital by Fama-French 12 Industry

Industry N % Mean Median COMPUSTAT %

BUSEQ 79 25.7% 0.166 0.150 16.6%

CHEMS 6 2.0% 0.118 0.120 1.8%

DURBL 3 1.0% 0.144 0.140 1.9%

ENRGY 11 3.6% 0.127 0.120 3.4%

HLTH 17 5.5% 0.115 0.103 9.4%

MANUF 51 16.6% 0.114 0.110 7.6%

MONEY 18 5.9% 0.137 0.130 32.2%

NODUR 27 8.8% 0.114 0.108 4.0%

SHOPS 17 5.5% 0.136 0.130 7.1%

TELCM 14 4.6% 0.144 0.118 3.1%

UTILS 7 2.3% 0.100 0.096 2.1%

OTHERS 57 18.6% 0.121 0.120 10.9%

Panel B Regression Analysis of Industry Cost of Capital ∑

Industry Parameter Estimates t-stat

Business Equipment (Intercept) 0.166*** 35.29

Chemicals and Allied Products -0.048*** -2.70

Consumer Durables -0.022 -0.90

Oil, Gas and Coal Extraction and Products -0.039*** -2.90

Healthcare, Medical Equipment, and Drugs -0.051*** -4.55

Manufacturing -0.052*** -6.87

Finance -0.029*** -2.66

Consumer Non-Durables -0.052*** -5.60

Wholesale, Retail, and Some services -0.030** -2.67

Telephone and Television Transmission -0.021* -1.77

Utilities -0.066*** -4.00

Other -0.045*** -6.20

R2 0.183 *, **, *** denotes significant (two-sided) at 1%, 5%, and 10%, respectively.

29

Table 3 Time Series of Cost of Capital

Chart

Summary Time-Series and Correlation

Year Cost of Capital

PEG SP 500 Investment Bond Yield

Speculative Bond Yield

2001 0.159 0.083 0.118 - -

2002 0.154 0.090 0.091 - -

2003 0.136 0.088 0.110 0.018 0.062

2004 0.113 0.088 0.120 0.014 0.041

2005 0.119 0.088 0.089 0.012 0.036

2006 0.120 0.085 0.083 0.013 0.036

2007 0.116 0.092 0.055 0.015 0.037

2008 0.142 0.095 -0.010 0.032 0.091

Corr(x,rate) - -0.08 -0.01 0.84** 0.92***

*, **, *** denotes significant (two-sided) at 1%, 5%, and 10%, respectively.

‐0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

2001 2002 2003 2004 2005 2006 2007 2008

Cost of Capital

Cost of Equity (PEG)

10‐year Moving Average S&P 500 Return

S&P Investment Grade Bond Yield

S&P Speculative Grade Bond Yield

30

Table 4 Determinants of Cost of Capital

Panel A Correlation ( N = 297 )

SIZE Q AGE CASH TAX LEV CFO5 EBIT σ(CFO)

RATE -0.25 0.26 -0.28 0.44 -0.25 -0.44 -0.16 -0.28 0.47

SIZE

0.22 0.24 -0.06# 0.11$ 0.13^ 0.24 0.34 -0.43

Q

0.03# 0.29 -0.08# -0.54 0.23 0.12^ 0.21

AGE

-0.12^ 0.22 0.04# 0.34 0.12^ -0.15

CASH

-0.13^ -0.56 -0.13^ -0.19 0.40

TAX

0.13^ 0.27 0.42 -0.18

LEV

-0.05# 0.16 -0.43

CFO5

0.40 -0.19

EBIT

-0.37

Panel B Multivariate Regression Analysis Ratet = α + Σβk·Xk,t-1 + εt

Variable Coefficient t-stat Coefficient t-stat

Intercept 15.26*** 9.68 14.11*** 12.65

SIZE -0.17 -1.27

Q 0.20 1.65

AGE -0.31*** -3.86 -0.36*** -4.81

CASH 0.37*** 3.59 0.36*** 3.58

TAX -0.11 -1.36

LEV -0.22* -1.68 -0.32*** -2.84

CFO5 -0.02 -0.18

EBIT -0.14 -1.08

σ(CFO) 0.43*** 3.50 0.56*** 5.23

FIRMWIDE -1.83*** -3.62 -1.96*** -3.90

N 297 297

Adj-R2 0.388 0.380

Notes to Table 4: See Appendix B for variable definitions. Annual decile rankings of determinant variables are used in the correlation and regressions. For Panel A, all correlations are significant at 1% except ^ (5%), $ (10%), and # (insignificant). For Panel B, all coefficients are multiplied by 100 for expositional convenience. *, **, *** denotes significant (two-sided) at 1%, 5%, and 10%, respectively.

31

Table 5 Determinants of Cost of Equity Capital

Panel A Descriptive Statistics of Sample

Variable N Mean Median Std Dev Q1 Q3

RATE 91 0.12 0.11 0.03 0.09 0.13

LEV 91 0.36 0.33 0.19 0.19 0.52

RATING 91 4.78 5.00 0.93 4.00 6.00

MV_EQ 91 7.07 2.40 15.15 0.61 6.30

BETA 91 1.13 1.04 0.62 0.76 1.48

BTM 91 0.77 0.58 0.84 0.36 0.83

RET 91 0.05 0.06 0.54 -0.22 0.28

Panel B Regression Analysis

RATEt = α0 + α1LEVt + β*RATINGt-1*LEVt + γ*KEt-1*(1-LEVt) + εt

Model 1 Model 2 Model 3 Model 4 Model 5

Intercept 0.017 0.091*** 0.142*** 0.153*** 0.029

(0.42) (6.17) (13.94) (13.36) (0.66)

LEV -0.193*** -0.201*** -0.259*** -0.272*** -0.171**

(-2.84) (-3.08) (-3.86) (-4.11) (-2.59)

RATING 0.055*** 0.038*** 0.041*** 0.040*** 0.048***

(4.73) (3.65) (3.65) (3.66) (4.32)

MV_EQ 0.014** 0.011**

(2.95) (2.38)

BETA 0.008*** 0.006***

(3.53) (3.15)

BTM -0.002 -0.002

(-0.98) (-1.06)

RET -0.004** -0.003**

(-2.03) (-2.05)

N 91 91 91 91 91

Adj-R2 0.196 0.226 0.125 0.155 0.298

Notes to Table 5: See Appendix B for variable definitions. Annual decile rankings of MV_EQ, BETA, BTM, and RET are used in the regressions. *, **, *** denotes significant (two-sided) at 1%, 5%, and 10%, respectively.

32

Table 6 Alternative Estimates of Cost of Equity

Panel A Descriptive Statistics of Sample

Variable N Mean Median Std Dev Q1 Q3 Corr

(Rate,X)

RATE 46 0.104 0.100 0.019 0.090 0.120

YIELD 46 0.068 0.070 0.006 0.067 0.073 0.107

WACC_PE 46 0.053 0.052 0.010 0.046 0.060 0.145

WACC_PEG 46 0.082 0.083 0.020 0.070 0.093 0.250*

WACC_MPEG 46 0.087 0.086 0.020 0.073 0.098 0.246*

Panel B Regression Analysis

RATEt = α0 + α1LEVt + β*RATINGt-1*LEVt + γ*KEt-1*(1-LEVt) + εt

Dependent Variable: Overall Cost of Capital

Intercept 0.111*** 0.123*** 0.122***

(6.89) (6.51) (6.22)

LEV -0.140** -0.155** -0.151**

(-2.33) (-2.05) (-2.14)

RATING 0.020* 0.021* 0.020*

(1.94) (1.76) (1.83)

KE_PE 0.176

(0.66)

KE_PEG -0.028

(-0.17)

KE_MPEG -0.017

(-0.10)

N 46 46 46

Adj-R2 0.129 0.120 0.120

Notes to Table 6: YIELD is average yield of all bonds in the same rating category at the beginning of current year. KE_PE, KE_PEG, and KE_MPEG are cost of equity estimated using the PE, PEG, and MPEG approach, respectively. WACC_PE, WACC_PEG, WACC_MPEG are weighted average cost of capital calculated using PE, PEG, and MPEG estimates of cost of equity, respectively. An effective tax rate of 40% is used when estimating WACC. *, **, *** denotes significant (two-sided) at 1%, 5%, and 10%, respectively.

33

Table 7 Cost of Capital and Investments

Panel A Descriptive Statistics of Sample

Variable N Mean Median Std Dev Q1 Q3 Corr

(CAPX,X)

CAPX 288 0.034 0.024 0.029 0.014 0.046

RATE 288 0.132 0.122 0.045 0.100 0.150 -0.144**

Q 288 1.581 1.283 1.093 1.015 1.808 0.164***

CFO5 288 0.063 0.065 0.082 0.044 0.101 0.154***

Panel B Regression Analysis: CAPXt~t+2 = β0 + β 1RATEt-1 + β 2Qt-1 + β 3CFO5t-1 + εt

Model 1 Model 2 Model 3 Model 4

Intercept 0.046*** 0.040*** 0.042*** 0.034***

(8.77) (7.18) (7.39) (5.75)

RATE -0.093** -0.103*** -0.080** -0.090**

(-2.46) (-2.76) (-2.12) (-2.40)

Q 0.005*** 0.005***

(3.08) (3.35)

CFO5 0.049** 0.055**

(2.33) (2.67)

N 288 288 288 288

Adj-R2 0.017 0.046 0.032 0.066

Notes to Table 7: See Appendix B for variable definitions. CAPX is measured at 1 year lag to cost of capital estimates. Tobin’s Q and CFO5 are measured at the same year of cost of capital. *, **, *** denotes significant (two-sided) at 1%, 5%, and 10%, respectively.